# Complex numbers

## Homework Statement

http://img139.imageshack.us/img139/999/ksknl6.th.jpg [Broken]http://g.imageshack.us/thpix.php [Broken]

Could someone confirm that the a) part is correct, and if it is, then what is the next step? :)
And im not exactly sure what to do in the b) part.

I would really appriciate if someone could help me out with this. :)

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HallsofIvy
Homework Helper
NO, (a) is not correct because you haven't answered the question! I think you have misunderstood what is asked. If you were asked to find $^4\sqrt{16}$, you wouldn't answer "161/4"!

Don't change from polar to rectangular form until after you have done the root! One important reason for using polar form for complex numbers is the fact that
$$[r (cos(\theta)+ i sin(\theta)]^n= r^n(cos(n\theta)+ i sin(n\theta))$$

For n= 1/4,
$$(7(cos(\pi/2)+ i sin(\pi/2))^{1/4}= 7^{1/4}(cos(\pi/8)+ i sin(\pi/8))$$
Also, since adding $2\pi$ to the argument doesn't change the complex number, and $2\pi/4= \pi/2$ another fourth root is
$$7^{1/4}(cos(\pi/4+ \pi/2)+ i sin(\pi/4+ \pi/2))$$
yet another is
$$7^{1/4}(cos(\pi/4+ \pi)+ i sin(\pi/4+ \pi))$$
and, finally,
$$7^{1/4}(coS(\pi/4+ 3\pi/2)+ i sin(\pi/4+ 3\pi/2))$$

Those are the four fourth roots of $7(cos(\pi/2)+ i sin(\pi/2))= 7i$

Nissen, Søren Rune
Edit: Shows what I know. Listen to HallsofIvy instead

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